If a quadratic equation has solutions, it should intersect the x-axis at least once.
A
a
Example Solution:
B
b
Example Solution:
Practice makes perfect
a
A quadratic equation can have 0, 1, or 2 solutions. Below, we see an example of a parabola with 1 solution at x=3, which means its vertex is on the x-axis.
b
A quadratic equation with no solutions occurs if we solve the left-hand side and right-hand side of an equation and it does not result in a solution. We see an example of this below.
x^2-6x+10=0
If we graph the left-hand side and right-hand side of this equation, we notice that the graphs do not intersect.
This is what is meant by a quadratic equation not having any solutions.
